Question

x4次方×（1－x²）最小值

Answer 1

X^2(1-X^2)

=4 (1/2X^2)(1/2X^2)(1-X^2)

≤4×［(1/2X^2+1/2X^2+1-X^2)/3］^3

=4×1/27

=4/27,

∴当且仅当1/2X^2=1-X^2,

X^2=2/3

X=±√6/3时,

原式最小=4/27.